This invention relates to reaction hydraulic turbines. More specifically, the invention relates to reaction hydraulic turbines with a radial intake having a spiral casing with inlet stay vanes, a radial guide gate apparatus with wicket gates, either a mixed flow runner or an axial flow runner with runner blades secured to the runner crown, and a draft tube with a cone and an elbow.
At any hydroelectric plant the water level in the upper reservoir varies in time. The upper reservoir level depends on the flow of the river on which the plant is situated and on the seasonal demand of the power grid supplied by the plant. Turbine head, denoted by Ht, varies along with the upper reservoir level.
Power output of a turbine, denoted by Pt, is continually adjusted to meet the immediate demand of the power grid. Thus, Pt is also a time dependent variable. Power output of a reaction hydraulic turbine is adjusted by changing the discharge angle of the wicket gates of the guide gate apparatus.
Power output of a turbine Pt (kW) is given by the following formula:Pt=gηtQtHt  (1)where:                ηt is the efficiency of the turbine,        Ht is the turbine head (m),        Qt is the flow rate through the turbine (m3/sec), and        g is gravitational acceleration (g=9.81 m/sec2).Formula (1) shows that, for a fixed value of Ht power output Pt is proportional to the flow rate Qt. The flow rate of the turbine can be adjusted by varying the wicket gate discharge angle α1. The wicket gate discharge angle is the angle of a wicket gate exit element relative to the circumference of the turbine. The flow rate of the turbine is an increasing function of the wicket gate discharge angle.        
The following considerations involve the concept of an elementary turbine. The flow inside the turbine passages is partitioned into thin laminated by axisymmetric stream surfaces of averaged meridional flow. An elementary turbine is the part of a turbine located in one such thin lamina.
For an elementary turbine the difference between the values of whirl at the wicket gate exit and at the runner blade exit, denoted by Δ(VuR), is given by Euler's equation:                               Δ          ⁡                      (                                          V                u                            ⁢              R                        )                          =                              g            ⁢                                                   ⁢                          η              t                        ⁢                          H              t                                ω                                    (        2        )            where ω is the angular velocity of the turbine (ω=πN/30, where N is the rotation rate of the turbine in rpm). Meanwhile, for the i-th elementary turbine, the value of whirl at the wicket gate exit, denoted by [(VuR)1]i, is given by[(VuR)1]i=[(VmR)1]i cot α1  (3)where [(VmR)1]i is the moment of velocity meridional component with respect the turbine axis at the wicket gate exit edge. Combining (2) and (3) one obtains the formula for whirl at the runner blade trailing edge for the i-th elementary turbine, denoted by [(VuR)2]i.                                           [                                          (                                                      V                    u                                    ⁢                  R                                )                            2                        ]                    i                =                                                            [                                                      (                                                                  V                        m                                            ⁢                      R                                        )                                    1                                ]                            i                        ⁢            cot            ⁢                                                   ⁢                          α              1                                -                                    g              ⁢                                                           ⁢                              η                t                            ⁢                              H                t                                      ω                                              (        4        )            
Formula (4) shows that for each elementary turbine the value of whirl at the runner blade exit varies with the values of Pt (via α1) and Ht. In particular, whirl does not necessarily vanish at the runner crown. If (VuR)2≢0 at the runner crown, an axial circular vortex forms at the runner crown tip. Otherwise Vu=(VuR)2/R would tend to infinity as R→0 leading to a contradiction (see L. M. Milne-Thomson, Theoretical Hydrodynamics, Macmillan [1960]).
The axial circular vortex core (0≦R≦Rcv, where Rcv is the core radius) rotates as a solid body with velocity:                               V          u                =                                            ω                              c                ⁢                                                                   ⁢                υ                                      ⁢            R                    2                                    (        5        )            where ωcv is distributed vorticity inside the core. The flow outside the axial circular vortex (R>Rcu) is similar to the flow after the runner blade trailing edge and has the same values of [(VuR)2]i, for the i-th elementary turbine. The axial circular vortex produces strong pulsations in draft tube. It ultimately dissipates due to the viscosity of water, causing a significant loss of head i turbine what results in a decrease of turbine efficiency given by:                               Δη                      c            ⁢                                                   ⁢            υ                          =                                            (                                                V                  u                                ⁢                R                            )                                      2              ⁢              c              ⁢                                                           ⁢              τ                        2                                2            ⁢                          gR              dt              2                        ⁢                          H              t                                                          (        6        )            where (VuR)2cr is whirl at the runner blade trailing edge in the elementary turbine adjacent to the runner crown and Rdt is the draft tube cone inlet radius (see G. I. Topazh, Computation of Integral Hydraulic Indicators of Hydromachines, Leningrad [1989]).
In order to avoid strong pulsation in draft tube and a loss efficiency due to the axial circular vortex in the design regime, turbines are designed to have (VuR)2cr=0 for the design values of power output (Pt)d and head (Ht)d. However, with variation of Ht and especially with variation of Pt, there is a significant loss of efficiency due to the axial circular vortex in prior art reaction hydraulic turbines with runner blades secured to the runner crown and having a draft tube with an elbow. For example, for a turbine with maximum efficiency ηmax=0.93, when Ht=0.80 (Ht)d and P5=0.50 (Pt)d, one may compute using (6) an efficiency loss of Δηcu=0.08 (i.e. 8%).
At this point Moody inventions (U.S. Pat. Nos. 1,769,887, July 1930, 1,848,738 March 1932, 1,848,739 March 1932, and 1,929,099, October 1933) should be mentioned. In all four these inventions Moody introduced draft tubes without an elbow and a horizontal diffuser.
Inside all Moody draft tubes there is a stationary pole mounted at the bottom. The pole is a geometrical continuation of the runner crown. The efficiency loss due to the axial circular vortex is eliminated in a reaction hydraulic turbine with runner blades secured to the runner crown and having one of Moody draft tubes. However, Moody draft tubes are inferior to the ones with an elbow and a horizontal diffuser and the turbine built with one of Moody draft tubes would have smaller efficiency at optimal operating regime.
For this reason turbines with Moody draft tubes with a stationary pole are not utilized at hydroelectric power plants.